You've just posted expressions for the final 3 integers, 39,41, and 55, and that means you're done. Very Nicely Done!

Just one little item I'd like to mention, you were not allowed to introduce any additional numerical digits, so I *removed* the zeroes from the final 3 expressions, but of course, that did not change how they calculated out.

Thanks a lot for running my challenge through your mental mill. I hope you had fun.

Just to throw a new spin onto this puzzle, I have seen this sort of thing before (although not this exact version), in which you use the digits of the current year (and try to get to 100). Admittedly, since 2000 this has probably become quite an interesting prospect, I originally got given the problem around 1993. I can't remember if I ever completed a year, but I had a go at them all at the time (and mostly gave up in 2000).

Joined: 19 May 2004Posts: 233Location: The beautiful city of Durham, well a nearby village anyway

Posted: Thu Aug 24, 2006 3:31 pm Post subject:

I'm quite amazed that you haven't seen the four fours problem before. I remember doing it as a homework task when I was 12 (2nd year high school). I've used it a few times with some of my classes - but I'm obviously mean to my kids - I won't let them use .4 and I get them to try to make all the numbers up to 100.

I'm guessing that that would only be allowed for 1-9 inclusive, with the question being interpreted as 'using only the individual digits, as numbers in their own right'. In which case, most 2-digit numbers, at least, seem to be completely impossible, at least using only the basic 4 operations, along with powers. In fact, the only one I can come up with (although I've not checked exhaustively, so I may have missed 1 or 2 ) is:

25=5^2

With more digits, of course, you have much more flexibility, so there would, I guess, be a reasonable, if modest, number of those. And if you start allowing factorials etc., then you can probably do a bit better.

It's an important function in analysis and heavy-lifting-style probability theory. But on the integers, it is defined as gamma(n) = (n-1)! A handy-dandy feature is that gamma(1/2)= sqrt(pi).

In reality, I would be more likely to spring the odd-factorial function on my teacher: n!! = (n)(n-2)...(2) if n is even, (n)(n-2)...(3)(1) if n is odd._________________There are only 10 kinds of people in the world--those who know binary, and those who don't.